Corrections & Clarifications: A previous version of this story misstated the number of miles of border fencing in the Big Bend Sector of west Texas.

President Donald Trump doubled down on his call for construction of a border wall Monday just hours after one U.S. Border Patrol agent was killed and another injured while working in a remote area of west Texas.

The Department of Homeland Security did not immediately say how Agent Rogelio Martinez was killed Sunday, but a Border Patrol spokesman said the incident did not involve an exchange of gunfire.

Authorities said the two agents were responding to activity along Interstate 10 near Van Horn, Texas, when they were injured. Martinez's partner, whose name was not immediately released, managed to put out a call for help. He was hospitalized in serious condition.

Speaking before a Cabinet meeting this morning, Trump said the second agent was brutally beaten and very, very badly hurt."

According to the Daily Caller, a Customs and Border Protection source said the agents were beaten with rocks, but that report has not been substantiated.

The FBI, responsible for investigating homicides involving federal officers, is working the case, said Jeanette Harper, a spokeswoman with the bureau's El Paso office. "They were not fired upon," Harper told the San Antonio Express-News. "There are so many different agencies working together that we need to come together and develop a timeline."

Meanwhile, investigators said they are searching for suspects or witnesses, but provided no further details.

Mexico’s ministry of foreign affairs issued a news release Monday offering condolences to Martinez’s family and offering to “collaborate with officials from the United States Department of Homeland Security if necessary.”

Overnight, Trump posted a tweet suggesting that Martinez's death solidifies his commitment to installing a 30-foot-tall barricade along the U.S.-Mexico border.

"We will seek out and bring to justice those responsible," the president wrote. "We will, and must, build the Wall!"

Border Patrol Officer killed at Southern Border, another badly hurt. We will seek out and bring to justice those responsible. We will, and must, build the Wall!

The two agents work in the Big Bend Sector of west Texas, among the most remote border zones and also one of the least traversed by smugglers and undocumented immigrants. The incident occurred near Van Horn, a town in the rugged Chihuahua Desert about 30 miles east of the border by air.

The 2,000-mile U.S.-Mexico border features 654 miles of pedestrian and vehicle fencing, but the Big Bend Sector — isolated and divided by sheer canyons of the Rio Grande — spans 510 miles of border and has just 5 miles of fencing.

That sector also is the least traveled by those crossing the border illegally. During 2016, Border Patrol agents apprehended just over 6,000 undocumented migrants and smugglers in the Big Bend Sector — about 12 per mile. One percent of all Border Patrol arrests occur in the sector, according to agency data.

Martinez, 36, had been a border agent since 2013.

“On behalf of the quarter of a million front line officers and agents of DHS, my thoughts and prayers go out to the family and friends of Agent Martinez and to the agent who is in serious condition," acting Secretary of Homeland Security Elaine Duke said in the statement.

U.S. Sen. Ted Cruz, R-Texas, said the event is “a stark reminder of the ongoing threat that an unsecure border poses to the safety of our communities and those charged with defending them. We are grateful for the courage and sacrifice of our border agents who have dedicated their lives to keeping us safe.”

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Three border wall prototypes are seen among the construction of the prototypes near the Otay Mesa Port of Entry outside of San Diego, California, as seen from behind the pre-existing border fencing on the international border between the U.S. and Tijuana, Mexico, on Oct. 16, 2017. David Wallace/The Republic

A border wall prototype is seen among the construction of the prototypes near the Otay Mesa Port of Entry outside of San Diego, California, as seen from Tijuana, Mexico, on Oct. 16, 2017. David Wallace/The Republic

Construction continues of the border wall prototype designed and contracted to Fisher Sand & Gravel of Tempe, among the construction of the prototypes near the Otay Mesa Port of Entry outside of San Diego, California, on Oct. 17, 2017. David Wallace/The Republic

Construction continues of the border wall prototype designed and contracted to Fisher Sand & Gravel of Tempe, among the construction of the prototypes near the Otay Mesa Port of Entry outside of San Diego, California, on Oct. 17, 2017. David Wallace/The Republic

Two border wall prototypes are seen among the construction of the prototypes near the Otay Mesa Port of Entry outside of San Diego, Calif., as seen from Tijuana, Mexico, on October 16, 2017. David Wallace/The Republic

A border wall prototype is seen among the construction of the prototypes near the Otay Mesa Port of Entry outside of San Diego, Calif., as seen from Tijuana, Mexico, on October 16, 2017. David Wallace/The Republic

A border wall prototypes is seen among the construction of the prototypes near the Otay Mesa Port of Entry outside of San Diego, Calif., as seen from Tijuana, Mexico, on October 16, 2017. David Wallace/The Republic

Two border wall prototypes are seen among the construction of the prototypes near the Otay Mesa Port of Entry outside of San Diego, Calif., as seen from Tijuana, Mexico, on October 16, 2017. David Wallace/The Republic

Three border wall prototypes are seen among the construction of the prototypes near the Otay Mesa Port of Entry outside of San Diego, Calif., as seen from behind the preexisting border fencing on the international border between the U.S. and Tijuana, Mexico, on October 16, 2017. David Wallace/The Republic

Three border wall prototypes are seen among the construction of the prototypes near the Otay Mesa Port of Entry outside of San Diego, Calif., as seen from behind the preexisting border fencing on the international border between the U.S. and Tijuana, Mexico, on October 16, 2017. David Wallace/The Republic

A border-wall prototype is seen among the construction of the prototypes near the Otay Mesa Port of Entry outside of San Diego, as seen from Tijuana, Mexico, on Oct. 16, 2017. David Wallace/The Republic

A border wall prototype is seen among the construction of the prototypes near the Otay Mesa Port of Entry outside of San Diego, Calif., as seen from Tijuana, Mexico, on October 16, 2017. David Wallace/The Republic

A border wall prototype is seen among the construction of the prototypes near the Otay Mesa Port of Entry outside of San Diego, Calif., as seen from Tijuana, Mexico, on October 16, 2017. David Wallace/The Republic

A border-wall prototype is seen among the construction of the prototypes near the Otay Mesa Port of Entry outside of San Diego, as seen from behind the pre-existing border fencing on U.S.-Mexico border on Oct. 16, 2017. David Wallace/The Republic

Two border wall prototypes are seen among the construction of the prototypes near the Otay Mesa Port of Entry outside of San Diego, Calif., as seen from behind the preexisting border fencing on the international border between the U.S. and Tijuana, Mexico, on October 16, 2017. David Wallace/The Republic